The partial table below shows the fraction of fish in Kathy's tank of different types. Type of fish Fraction of total Tetras $\dfrac16$ Guppies $\dfrac25$ Goldfish $\dfrac14$ $\dots$ $\dots$ What fraction of Kathy's fish are either tetras or guppies?
We can add to find the fraction of Kathy's fish that are either tetras or guppies. $\frac{1}{6}$ $\frac{2}{5}$ $\frac{1}{4}$ Tetras Guppies Goldfish Other fish Tetras or guppies All fish in tank 1 6 + 2 5 = total tetras & guppies {\dfrac{1}{6}}+{\dfrac{2}{5}}=\text{total tetras & guppies} Our denominators need to be the same so we can add. What is the least common multiple for the denominators $6$ and ${5}$ ? The least common multiple of $6$ and ${5}$ is ${30}$. $\dfrac{{1}\times 5}{{6}\times 5} = {\dfrac{5}{30}}$ $\dfrac{{2}\times 6}{{5}\times 6} = {\dfrac{12}{30}}$ Now, we can add our fractions. $\begin{aligned}{\dfrac{5}{30}} + {\dfrac{12}{30}} &= \dfrac{{5} + {12}}{30} \\\\ &= \dfrac{17}{30}\end{aligned}$ $\dfrac{17}{30}$ of Kathy's fish are tetras or guppies.